Images obtained from image sensing devices always contain noise to some extent. In the application field of medical Rx-imaging there exists a well known tradeoff between diagnostic image quality and patient dose, due to the presence of noise in the radiation source.
Linear and nonlinear filters are widely used in image processing applications to reduce the noise level. Linear filters perform very well in attenuating the noise component, but at the same time this category of filters smear the edges and small structures within the image. In this respect many nonlinear filters preserve edges much better, such as described in the paper: Fong Y. S., Pomalaza-Raez C. A., Wang X. H., "Comparison study of nonlinear filters in image processing applications", Optical Engineering, vol. 28, no. 7, pp. 749-760, July 1989.
Ideally the filter parameters should be adjusted to the local image statistics. A basic adaptive noise filtering method is described in: Lee J. S., "Digital Image Enhancement and Noise Filtering by use of Local Statistics", IEEE Trans. on Pattern Analysis and Machine Intelligence, vol. 2, no. 2, pp. 165-168, March 1980. Typically the local variance is used to control the degree of smoothing.
Until now research on noise filtering in place domain was focused on local operators with a fixed size. These kind of filters perform optimally only if the noise spatial spectrum is confined to a narrow band, usually the higher frequency portion of the image spectrum. If the noise band is not very narrow, larger filter sizes must be used, and artifacts are likely to occur in regions of abruptly changing statistics such as in the vicinity of edges. Filters known as `sigma filter`, or `adaptive mean filter` as they are called in the above comparative study of Wong et al. provide a solution to this problem, but they are computationally expensive.
In the field of digital image processing a novel paradigm of multiresolution computation has evolved the last decade, sometimes called pyramidal image processing. According to this concept multiple sets of processing parameters are used, tuned to a wide range of detail sizes. The basic concepts and efficient implementations of pyramidal decomposition are described in: Burt P. J., "Fast Filter Transforms for Image Processing", Computer Graphics and Image Processing, vol. 16, pp. 20-51, 1981; Crowley J. L., Stern R. M., "Fast Computation of the Difference of Low-Pass Transform", IEEE Trans. on Pattern Analysis and Machine Intelligence, vol. 6, no. 2, ; March 1984.
Alternative multiresolution representations are presented in: Mallat S. G., "A Theory for Multiresolution Signal Decomposition: The Wavelet Representation", IEEE Trans. on Pattern Analysis and Machine Intelligence, vol. 11, no. 7, July 1989; Ebrahimi T., Kunt M., "Image compression by Gabor Expansion", Optical Engineering, vol. 30, no. 7, pp. 873-880, July 1991.
Until now the main purpose of these kind of image processing techniques has been directed towards image compression.
Other applications include multiresolution image segmentation, image interpolation, and filter synthesis with specified frequency response. A novel application of multiresolution decomposition for the purpose of contrast enhancement is disclosed in an unpublished european patent application 91202079.9 filed Aug. 14, 1991.
A multiresolution noise filtering algorithm is proposed in: Ranganath S., "Image Filtering Using Multiresolution Representations", IEEE Trans. on Pattern Analysis and Machine Intelligence, vol. 13, no. 5, pp. 426-440, May 1991. According to the paradigm described in this paper, a sequence of low pass approximations of the original image at successively coarser resolution levels are computed, and adaptive noise suppression is achieved by linearly combining all levels at every pixel position, the weight coefficients being adapted to the local noise statistics at every pixel.
In Pattern Recognition Letters, vol. 12, no. 8 of August 1991 an article entitled `Edge preserving artifact free smoothing with image pyramids` has been published. This article discloses a smoothing method in which smoothing is performed by assigning the local mean of non-overlapping pixel blocks of sizes either 8.times.8, 4.times.4, or 2.times.2 to all pixels of the block, depending on whether the block is homogeneous or not (assignment starting with the larger block sizes). Pixels which do not belong to a homogeneous block of any size are assigned a value which is a weighted average of the input pixel value and the 2.times.2 local mean. Assigning identical values to blocks of pixels inherently causes so called "block artifacts", a problem being recognized in the same reference.